No, it has nothing to do with Act of "God" (if you believe in that). Just because it happened in their vehicle does not at all make them liable. And that has nothing to do with my being an openly admitted Disney "apologist". From a pure legal liability standpoint, if the CMs were following proper protocol, there is no liability on Disney. I do auto and general liability (slip and fall, food poisoning, etc...) insurance for a living. Certainly haven't come across WDW tram claims, but have countless ones with somewhat similar circumstances. Just because you are injured in a vehicle someone else was driving does not make them liable. Disney can, and likely would, offer to pay a medical bill as a customer service gesture. There's actually specific insurance for that, called MEDPAY. It provides coverage for a small amount of medical bills even if the business isn't liable. Lots of businesses have that. That would be the case here. From what OP posted, a guest did something that could be dangerous and is obviously a clear violation of WDW rules. The CM (I'm guessing) has protocol to tell the driver to stop. The driver (again guessing) has no idea why they are told to stop, only that something is wrong. They come to an immediate halt. Where is liability on Disney? I can tell you it wouldn't hold water in court, if those are the true facts.
EDIT: Best comparable example I can think of that I've dealt with over and over and over is on school buses. A child is standing up in their seat...or even sitting in it. The driver has to slam on the brakes for any variety of reasons. No actual accident occurs, just the driver hitting the brakes hard, or maybe making a turn while a child stands up. Child bumps the seat or falls and gets checked out by the doctor. The school district will carry insurance to pay the medical bills as a gesture of good will, but legal liability is outright denied.